Nonperturbative gravity corrections to bulk reconstruction

TL;DR

This paper develops a new algebraic framework for bulk reconstruction in holography, incorporating nonperturbative gravitational effects and demonstrating state-independent recovery of local operators within the reconstruction wedge.

Contribution

It introduces a novel algebraic approach that accounts for nonperturbative gravitational errors and proves the bulk reconstruction wedge satisfies the properties of a quantum error-correcting code.

Findings

Reconstruction wedge satisfies bulk reconstruction with nonperturbative errors

Local operators in the wedge can be recovered state-independently

Uses twirled Petz map for universal recovery channel

Abstract

We introduce a new algebraic framework for understanding nonperturbative gravitational aspects of bulk reconstruction with a finite or infinite-dimensional boundary Hilbert space. We use relative entropy equivalence between bulk and boundary with an inclusion of nonperturbative gravitational errors, which give rise to approximate recovery. We utilize the privacy/correctability correspondence to prove that the reconstruction wedge, the intersection of all entanglement wedges in pure and mixed states, manifestly satisfies bulk reconstruction. We explicitly demonstrate that local operators in the reconstruction wedge of a given boundary region can be recovered in a state-independent way for arbitrarily large code subspaces, up to nonperturbative errors in $G_N$. We further discuss state-dependent recovery beyond the reconstruction wedge and the use of the twirled Petz map as a universal recovery channel. We discuss our setup in the context of quantum islands and the information paradox.